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# 08.06 Module Eight Activity

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## Varsha Parthasarathy

on 29 July 2016

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#### Transcript of 08.06 Module Eight Activity

Step 1: Calculations
The medical pool tank will be a cylinder. I used 9 ft. as the radius of the pool, and 72 ft. for the height. Anything larger than that would exceed the limit for the tank. So the volume of the cylinder is:

V = π x r^2 x h
V = π x (9)^2 x (72)
V = 18,321.76836 Which is less than 21,206
The stadium is in need of a medical pool to attend to injured or sick whales. The pool will be located adjacent to the holding tanks. Your job is to design a medical pool using a 3-dimensional polyhedral shape you learned about in this module. For safety reasons, the tank can be no more than one-fourth the volume of a holding tank. You will need to submit a 2-dimensional drawing, the dimensions, the volume of your pool, and proof that the pool's volume is no more than one-fourth the volume of a holding tank to your instructor.
Main Show Tank Calculation:
1.) The main tank has a radius of 70 feet. What is the volume of the quarter-sphered sized tank? Round your answer to the nearest whole number. You must explain your answer using words, and you must show all work and calculations to receive credit.

The volume of a sphere: Volume of quarter-sphered tank:

V = 4/3 x π x r^3 V = 1/4 x 1436755.04
V = 4/3 x π x (70)^3 V = 359,188.76
V = 1,436,755.04

Volume of the quarter-sphered sized tank rounded to the nearest whole number: 359,189 ft.^3

Holding Tank Calculations:

The holding tanks are congruent in size, and both are in the shape of a cylinder that has been cut in half vertically. The bottom of the tank is a curved surface. What is the volume of both tanks if the radius of tank #1 is 15 feet and the height of tank #2 is 120 feet? You must explain your answer using words, and you must show all work and calculations to receive credit.

The volume of a cylinder:

V = π x r^2 x h T
hey are both in the shape of a cylinder that has been cut in half vertically, and
V = π x (15)^2 x (120)
they are also congruent.
V = 84,823.00165

Volume of both tanks: 84,823.00165 ft.^3
Rounded Volume: 84,823 ft.^3

Density Calculation:

In step 1, you found the volume (in cubic feet) of the main tank. If the maximum density of killer whales per cubic foot is 0.000011142, what is the maximum number of killer whales allowed in the main show tank at any given time? You must explain your answer using words, and you must show all work and calculations to receive credit.

The maximum density of killer whales per cubic foot is 0.000011142, and the volume of the main tank is 359,189 ft. ^3. Density = Mass / Volume. So 0.000011142 = Mass / 359,189.

Mass = 0.000011142 x 359,189
Mass = 4.002083838

The maximum number of killer whales allowed in the main show tank: 4

Step 3: Reflections
08.06 Module Eight Activity
Step 2: Design
Medical Pool
72 ft.
9 ft.
1/4 the volume of a holding tank:
84,823 / 4 = 21,205.75
The pool can't have a volume
greater than 21,206.
5.) The theme park company is building a scale model of the killer whale stadium main show tank for an investor's presentation. Each dimension will be made 6 times smaller to accommodate the mock-up in the presentation room. How many times smaller than the actual volume is the volume of the mock-up?
6.) Using the same information from #5, what percent of change occurred from the actual tank to the mock-up of the tank?
7.) If you were to take a cross section parallel to the base of one of the holding tanks, how would you describe the shape?
Samples of the tank's water are taken daily to ensure the salt density is correct to maintain aquatic life. The following chart shows the past 2 days' samples:
Describe the information in the chart using words. What do you think the information shown means? If you were in charge of the killer whale tank, what action might you take after seeing the samples shown above?
If the mock-up is 6 times smaller than the actual stadium, then the radius of the mock-up would be 70/6 which equals 11.66666667. And I rounded it to 11.67. So the volume of the mock-up would be:

V = 4/3 x π x r^3
V = 4/3 x π x (11.67)^3
V = 6657.346743 You still have to divide by 4.
6657.346743 / 4 = 1664.336686

Volume of the mock-up: 1,664.336686

The actual volume is 359,188.76.

359,188.76 / 1,664.336686 = 215.8149628

The actual volume is about 216 times larger than the volume of the mock-up

The actual volume is about 216 times larger than the volume of the mock-up

So 216 x 100 = 21,600%

There was 21,600% of change from the actual tank to the mock-up tank.
Since the base of a holding tank is curved, and also since it is a cylinder, a cross section parallel to the base of one of the holding tanks would make a sphere.
The information in the chart shows that the grams of salt per liter of seawater, and the approximate density are both decreasing. The normal condition to maintain aquatic life is not met in the killer whale tanks. This can affect the killer whales in the tank. I would immediately put 35g of salt per liter of saltwater and set a density of 3.5% in each tank.
Height: 120 ft.
Height: 120 ft.